High-speed laser frequency actuation is critical in all applications employing lasers and frequency combs, and is prerequisite for phase locking, frequency stabilization and stability transfer among multiple optical carriers. Soliton microcombs have emerged as chip-scale, broadband and low-power-consumption frequency comb sources.Yet, integrated microcombs relying on thermal heaters for on-chip actuation all exhibit only kilohertz actuation bandwidth. Consequently, high-speed actuation and locking of microcombs have been attained only with off-chip bulk modulators. Here, we present high-speed microcomb actuation using integrated components. By monolithically integrating piezoelectric AlN actuators on ultralow-loss Si3N4 photonic circuits, we demonstrate voltage-controlled soliton tuning, modulation and stabilization. The integrated AlN actuators feature bi-directional tuning with high linearity and low hysteresis, operate with 300 nW power and exhibit flat actuation response up to megahertz frequency, significantly exceeding bulk piezo tuning bandwidth. We use this novel capability to demonstrate a microcomb engine for parallel FMCW LiDAR, via synchronously tuning the laser and microresonator. By applying a triangular sweep at the modulation rate matching the frequency spacing of HBAR modes, we exploit the resonant build-up of bulk acoustic energy to significantly lower the required driving to a CMOS voltage of only 7 Volts. Our approach endows soliton microcombs with integrated, ultralow-power-consumption, and fast actuation, significantly expanding the repertoire of technological applications.